I didn't know how to store the value, with just month and year, so I decided to use varchar type. From there I decided if I wanted to perform date query commands, I would have to convert it from a string to date. One query I'd like to perform is finding out which faculty ID is associated with dates after 1991.

I used the following to_date function to convert the string to date:
UPDATE qualified SET dq2 = to_date(datequalified, 'MM\YYYY')

the dq2 column was output as the following:

dq2
1995-09-01
1991-09-01
1988-09-01
1991-09-01
1988-09-01
1996-09-01

Is it possible to get dq2 output as just month and year, and still permit, date related queries?